In October of 2013, the federal government shut down for 16 days — the third longest shutdown in history. A few women in particular came together to end the gridlock, including Maine Republican Sen. Susan Collins and Minnesota Democrat Sen. Amy Klobuchar.

"The truth is, women in the Senate is a good thing," he said. "And we're all just glad that they allowed us to tag along so we can see how it's done. Isn't that right?"

The whole episode fed into a pervasive idea: that women lawmakers are better at bipartisan compromise than men are.

With a record number of women running for Congress, there's a decent chance that the number of women on Capitol Hill will grow next session. That could be a hugely important change, as women remain heavily underrepresented in Congress, making up 1 in 5 lawmakers, even as they make up more than half of voters.

However, there's little reason to expect it will make Congress more bipartisan, according to a new study.

"Women and men are first and foremost partisans," said Jennifer Lawless, a professor of politics at the University of Virginia.

She and coauthors Sean Theriault and Samantha Guthrie studied how big the gap is between how likely women and men lawmakers are to reach across the aisle.

As it turns out, that gender gap is very, very small.

"We found virtually no gender differences," Lawless said.

That lack of a gender gap persisted across a number of measures: different types of votes, the amendment process, even official travel.

"Women were no more likely than men to take bipartisan fact-finding missions abroad," Lawless explained. "They were no more likely than men to cosponsor legislation from someone of the other party. They were no more likely than men to cast bipartisan procedural votes, and we've known for a long time they were no more likely to vote differently on substantive final votes."

There are real reasons why this stereotype exists. One is those high-profile examples, like the 2013 shutdown. Another is that women do cooperate well... when they're not elected officials.

"Outside of politics, there's a lot of evidence from a lot of different disciplines that women actually are more likely than men to value cooperation and collaboration," Lawless said.

In addition, there are high-profile women lawmakers who are known for being moderates — Collins perhaps chief among them.

"It's hard to disentangle gender and ideology. So when we talk about women being more collegial, we automatically think about Susan Collins and Lisa Murkowski and Claire McCaskill and people like this, and those people are moderates," said Michele Swers, a professor of American government at Georgetown University, who has written or co-written three books on women and politics.

But while lawmakers like Collins are often cited as examples of bipartisan women, there are also high-profile moderate men like Arizona Republican Sen. Jeff Flake and Tennessee Republican Sen. Bob Corker. In addition,plenty of other, less-moderate women never make it into that conversation.

"For example, nobody would have described Barbara Boxer or Elizabeth Warren as bipartisan, right?" Swers said.

It's possible that the Senate — which is immune to gerrymandering — fosters a more collegial atmosphere, Swers said.

But the bottom line is that partisanship creates incentives that keep women and men voting in much the same ways.

"Party loyalty is what's valued. Party loyalty is how you climb the ladder. Party loyalty is how you get the committee assignments you want. Party loyalty is how you get reelected," Lawless said.

And so, while voters might pay lip service to bipartisanship, their voting patterns often end up proving otherwise.

"We have such partisan districts right now that if you are engaging in bipartisanship, although voters say they want more collaboration and cooperation, they want to make sure that their members of Congress are representing their districts," Lawless added.

The (very old) idea of women as morally superior

The idea that women are naturally suited to cleaning up the messy business of politics is an old one, according to former Democratic congresswoman Pat Schroeder.

"This goes way back to when women got the right to vote," she said. "Many people thought, 'Oh, if women are voting there'll be more morality. It'll be wonderful and the angels will descend from heaven.'"

Examples of this idea — that women's moral superiority would improve politics — are not difficult to find in early-20th-century writings. As one judge put it in the American Journal of Nursing in 1909: "If the women alone had a vote, it would result in a class of men in public office whose character for morality, honesty and courage would be of a much higher order."

But even sexism that seems to benefit women can damage them in the long term.

"I worry that we're setting a bar for women that they'll never be able to meet," Lawless said. "If part of the reason that people are thinking we should elect more women are we should recruit more women to run for office because they can go to Washington and fix everything that's broke."

Women lawmakers still govern differently than men do

Even if women don't take more bipartisan actionsthan men, that doesn't mean women and men govern in exactly the same ways. Far from it.

After decades on Capitol Hill, Schroeder does see some differences in how women and men in Congress do their jobs.

"I do think that women are much more in tune to working family issues just because of where they come from," she said.

And research bears this out. For example, when earmarks — a tool for lawmakers to designate spending for specific projects, often in their districts — were still allowed, women legislators were more likely than men to request earmarks for promoting women's health and combating violence against women. Another study found that women lawmakers are more likely than men to introduce bills in what researchers called "women's issues" areas, including health, education, and civil rights.

According to one expert, the differences are particularly pronounced among Democrats.

"The women in the Democratic Party seem to be even more committed to issues that people think of as related to women children and families — women's rights issues, equal pay, these kinds of things," Swers said. "Democratic men support these things, too. But Democratic women are more likely to use their political capital to write the bills to build the support to sign on as cosponsors to these types of things."

The gender differences go beyond issues — it's possible that women legislators simply legislate differently from men. Republican Connie Morella, who served in the House from 1987 through 2003, believes that.

"I think that women come to it having worked harder to reach that point," she said. "They tend to persevere more, they tend to have more patience, and I think their mandate to themselves is, 'Let's get things done.'"

And there is some evidence that women lawmakers are particularly good at getting things done. Studies have shown that women legislators bring more spending back to their districts than men. Minority-party women have also been shown to be better than men at keeping their bills alive longer.

The question is why that happens. The connection that Morella made — between women having to overcome sexism and their performance in office — has been called the "Jill Robinson effect," a phenomenon named after Jackie Robinson, who became a baseball superstar despite overwhelming racism.

The idea is that, if there's sexism in politics (or if women candidates perceive sexism), only the most qualified, motivated women will get involved and win, meaning those women will end up being more effective, on average, than men, who don't have to overcome the same hurdles.

Does socializing improve anything?

Regardless of what studies might say, Morella says she saw women lawmakers being more bipartisan than men.

"I do think that working together is something that women — whether they think about it or not, whether it is important to them — it's one of their priorities," she said. "I found that to be the case."

But then, it's also true that Congress has changed since Morella left office in 2003, growing ever more polarized.

"As women's presence in Congress has increased, so has party polarization. That's certainly not to suggest that women are the cause of it, but it does send a pretty clear message that they're not inoculating the institution from it," Lawless said.

She and her coauthors did find one difference between men and women lawmakers: women in Congress participate in organized social activities more often than men do.

"It's very possible that Congress would function even worse if we didn't have women in there right now," she said. "Women are the social glue that holds the institution together."

Playing softball together and doing secret Santas may be ways in which women are creating a more civil atmosphere on Capitol Hill. There's no way to know if this has absolutely zero effect on how bipartisan deals are made — for example, it might affect dealmaking within parties — but it doesn't seem to affect voting across party lines.

Lawless' study is certainly not the first time that academics have studied bipartisanship and gender. As recently as 2016, a group of researchers found that "women are indeed more likely to cooperate across party lines, but only if they're Republican, and particularly if they're working on a bill that focuses on health, education, or social welfare," as The Atlantic's Andrew McGill wrote at the time.

This newest study doesn't necessarily contradict those findings, Lawless says. What her study shows, she says, is that even if bipartisan happens in very specific cases, it doesn't happen systemically or consistently.

The idea that being a woman makes someone a better lawmaker does pop up occasionally on the campaign trail, like in an ad from Arizona Republican Senate candidate Martha McSally, in which the former fighter pilot boasts, "I told Washington Republicans to grow a pair of ovaries and get the job done."

Then again, she's not exactly making a bipartisan appeal here. Later in the ad, she proclaims, "After taking on terrorists, the liberals in the Senate won't scare me one bit."

At a time when Congress is as polarized as ever, trying to tell voters you'll reach across the aisle just may not be a winning strategy — whether you're a man or a woman.